Phononic Band Gap Materials Research Articles

Complex role of strain engineering of lattice thermal conductivity in hydrogenated graphene-like borophene induced by high-order phonon anharmonicity

Strain engineering has been used as a versatile tool for regulating the thermal transport in various materials as a result of the phonon frequency shift. On the other hand, the phononic bandgap can be simultaneously tuned by the strain, which can play a critical role in wide phononic bandgap materials due to the high-order phonon anharmonicity. In this work, we investigate the complex role of uniaxial tensile strain on the lattice thermal conductivity of hydrogenated graphene-like borophene, by using molecular dynamics simulations with a machine learning potential. Our findings highlight a novel and intriguing phenomenon that the thermal conductivity in the armchair direction is non-monotonically dependent on the uniaxial armchair strain. Specifically, we uncover that the increase of phonon group velocity and the decrease of three-phonon scattering compete with the enhancement of four-phonon scattering under armchair strain, leading to the non-monotonic dependence. The enhanced four-phonon scattering originates from the unique bridged B–H bond that can sensitively control the phononic bandgap under armchair strain. This anomalous non-monotonic strain-dependence highlights the complex interplay between different mechanisms governing thermal transport in 2D materials with large phononic bandgaps. Our study offers valuable insights for designing innovative thermal management strategies based on strain.

Tunable phononic bandgap materials designed via topology optimization

Topology optimization is used to design phononic bandgap materials that are tunable by mechanical deformation. A periodic media is considered, which due to the assumption of length scale separation, allows the dispersion relations to be obtained by analyzing a single unit cell subjected to Floquet–Bloch boundary conditions. A finite macroscopic deformation is applied to the unit cell to affect its geometry and hence dispersion. We tune the dispersion–deformation relation to our liking by solving a topology optimization problem using nonlinear programming. The adjoint method is employed to compute the sensitivities, and the non-differentiability of degenerate eigenvalues is avoided using symmetric polynomials. Several tunable phononic crystal designs are presented. Also, a verification analysis is performed, wherein the optimized design is interpreted and analyzed using a conforming finite element mesh.

Comparison of Transmission Measurement Methods of Elastic Waves in Phononic Band Gap Materials.

Periodic cellular structures can exhibit metamaterial properties, such as phononic band gaps. In order to detect these frequency bands of strong wave attenuation experimentally, several devices for wave excitation and measurement can be applied. In this work, piezoelectric transducers are utilized to excite two additively manufactured three-dimensional cellular structures. For the measurement of the transmission factor, we compare two methods. First, the transmitted waves are measured with the same kind of piezoelectric transducer. Second, a laser Doppler vibrometer is employed to scan the mechanical vibrations of the sample on both the emitting and receiving surfaces. The additional comparison of two different methods of spatial averaging of the vibrometer data, that is, the quadratic mean and arithmetic mean, provides insight into the way the piezoelectric transducers convert the transmitted signal. Experimental results are supported by numerical simulations of the dispersion relation and a simplified transmission simulation.

Multiobjective Optimization of Two-Dimensional Phononic Bandgap Materials and Structures Using Genetic Algorithms

In this paper, two-dimensional phononic bandgap materials are designed through multiobjective optimization using the genetic algorithm. Two cases are given. In Case I, 2D phononic crystals (PnCs) with maximum bandgap and minimum mass are optimized. The optimal results show that the third-order relative bandgaps become large, along with the increase in mass. In Case II, 2D local resonance phononic crystals (LRPnCs) simultaneously maximizing the third and sixth relative bandgap widths (RBWs) are designed. The frequency response function of the optimized structures shows that the attenuation of elastic waves is most remarkable at the beginning frequency of the bandgap. Finally, an integrated structure, which accumulates the bandgaps of three optimized substructures, is proposed. These results provide a new approach for bandgap design.

Three-Phase Microstructure Topology Optimization of Two-Dimensional Phononic Bandgap Materials Using Genetic Algorithms

The bandgap, an important characteristic of the periodic structure, is dispersion-related, which can be designed by tailoring the layout of materials within the periodic microstructures. A typical example of a periodic structure is phononic crystals (PnCs), which are traditionally fabricated from two-phase materials. Herein, we investigate the topologies of periodic three-phase PnCs. The microstructures of the three-phase PnCs are optimized using a two-stage genetic algorithm, and three case studies are proposed to obtain the following: (1) the maximum relative bandgap width, (2) the maximum absolute bandgap width, and (3) the maximum bandgap at a specified frequency. More importantly, the three-phase material provides significant advantages compared to the typical two-phase materials, such as a low-frequency bandgap. This research is expected to contribute highly to vibration and noise isolation, elastic wave filters, and acoustic devices.

Single phase 3D phononic band gap material

Phononic band gap materials are capable of prohibiting the propagation of mechanical waves in certain frequency ranges. Band gaps are produced by combining different phases with different properties within one material. In this paper, we present a novel cellular material consisting of only one phase with a phononic band gap. Different phases are modelled by lattice structure design based on eigenmode analysis. Test samples are built from a titanium alloy using selective electron beam melting. For the first time, the predicted phononic band gaps via FEM simulation are experimentally verified. In addition, it is shown how the position and extension of the band gaps can be tuned by utilizing knowledge-based design.

A Gradient-Based Optimization Method for the Design of Layered Phononic Band-Gap Materials

Phononic materials with specific band-gap characteristics at desired frequency ranges are in great demand for vibration and noise isolation, elastic wave filters, and acoustic devices. The attenuation coefficient curve depicts both the frequency range of band gap and the attenuation of elastic wave, where the frequency ranges corresponding to the none-zero attenuation coefficients are band gaps. Therefore, the band-gap characteristics can be achieved through maximizing the attenuation coefficient at the corresponding frequency or within the corresponding frequency range. Because the attenuation coefficient curve is not smooth in the frequency domain, the gradient-based optimization methods cannot be directly used in the design optimization of phononic band-gap materials to achieve the maximum attenuation within the desired frequency range. To overcome this difficulty, the objective of maximizing the attenuation coefficient is transformed into maximizing its Cosine, and in this way, the objective function is smoothed and becomes differentiable. Based on this objective function, a novel gradient-based optimization approach is proposed to open the band gap at a prescribed frequency range and to further maximize the attenuation efficiency of the elastic wave at a specific frequency or within a prescribed frequency range. Numerical results demonstrate the effectiveness of the proposed gradient-based optimization method for enhancing the wave attenuation properties.

Pareto optimal design of layered bandgap materials with multiphase microstructures using evolutionary algorithms

An important characteristic of the periodic materials or structures is the existence of bandgap. This bandgap, which is dispersion-related, can be designed by controlling the materials layout within the periodic microstructures. In this paper, the topologies of periodic multiphase microstructures are optimized using a multiobjective genetic algorithm and two cases of studies are presented. The results show that 3-phase material can obtain quite better designs on the basis of fewer layers. This will be a reference for the design of phononic bandgap materials.

Effects of material parameters on elastic band gaps of three-dimensional solid phononic crystals

In this paper, we study the influences of material parameters on the phononic band gaps of three-dimensional (3D) solid phononic crystals (PCs) based on the finite difference time domain (FDTD) method. We begin with the basic wave equations and the FDTD formulation to derive the material parameters directly determining the band gaps of the 3D solid PCs. The parameters include the transverse velocity ratio, the acoustic impedance ratio and the Poisson ratios (or equivalently, the mass density ratio, the shear modulus ratio and the Poisson ratios) of the scatterers and host materials. The negative Poisson ratio is also considered in our investigation. The effects of these material parameters on band gap width are discussed based on detailed numerical calculations for systems with three typical lattices. The generation mechanism of band gaps (Bragg scattering or local resonance) which is determined by the material parameters is also discussed. The analysis is expected to be applied to the artificial design of 3D phononic band gap materials.

Enhancement of phononic band gaps in ternary/binary structure

Abstract Based on the transfer matrix method (TMM) and Bloch theory, the interaction of elastic waves (normal incidence) with 1D phononic crystal had been studied. The transfer matrix method was obtained for both longitudinal and transverse waves by applying the continuity conditions between the consecutive unit cells. Dispersion relations are calculated and plotted for both binary and ternary structures. Also we have investigated the corresponding effects on the band gaps values for the two types of phononic crystals. Furthermore, it can be observed that the complete band gaps are located in the common frequency stop-band regions. Numerical simulations are performed to investigate the effect of different thickness ratios inside each unit cell on the band gap values, as well as unit cells thickness on the central band gap frequency. These phononic band gap materials can be used as a filter for elastic waves at different frequencies values.

Band Gaps and Single Scattering of Phononic Crystal

A method is introduced to study the transmission and scattering properties of acoustic waves in two–dimen- sional phononic band gap (PBG) materials. First, it is used to calculate the transmission coefficients of PBG samples. Second, the transmitted power is calculated based on the far field approach. We have also calcu- lated the scattering cross section, the results indicate that phononic band gap appear in frequency regions between two well separated resonance states.

Hypersonic Modulation of Light in Three-Dimensional Photonic and Phononic Band-Gap Materials

The elastic coupling between the a-SiO2 spheres composing opal films brings forth three-dimensional periodic structures which besides a photonic stop band are predicted to also exhibit complete phononic band gaps. The influence of elastic crystal vibrations on the photonic band structure has been studied by injection of coherent hypersonic wave packets generated in a metal transducer by subpicosecond laser pulses. These studies show that light with energies close to the photonic band gap can be efficiently modulated by hypersonic waves.

Delocalization of phonons and quantized thermal conductance in a randomn-mer system

In this paper we report the phononic transport and its influence on thermal conductance in a one-dimensional random $n$-mer system. Based on an elastic wave equation, we studied frequency spectrum, phononic transmission, and thermal conductivity of the system. Multiple resonant transmissions are observed, which originate from delocalization of phonons in the correlated disorder system. At each resonant mode, zero-Lyapunov exponent and undecayed vibration of atoms have been found through the whole chain. Meanwhile channels are opened for phonon transmission and heat transport. As a result, thermal conductance is significantly enhanced at each resonant mode, forming a quantized feature as frequency increases. These properties demonstrate the possibility of manipulating phonon propagation and thermal conductance in phononic bandgap materials and may have potential applications in designing filter and waveguide for acoustic waves.

Transmission and scattering properties of acoustic waves in phononic band gap materials

We have developed a formula for studying the transmission and scattering properties of finite-sized phononic band gap (PBG) material. We will show that based on the far field approach the transmission coefficients can be obtained by treating PBG samples as scattering objects. We find that the results agree well with the band structure.

Transmission and dispersion relations of perfect and defect-containing waveguide structures in phononic band gap materials

By using a combination of finite difference time domain (FDTD) and plane wave expansion (PWE) methods, we study the propagation of acoustic waves through waveguide structures in phononic band gap crystals composed of solid constituents. We investigate transmission through perfect linear waveguides, waveguides containing a resonant cavity, or waveguides coupled with a side branch resonator such as a cavity or a stub. A linear guide can support one or several modes falling in the absolute band gap of the phononic crystal. It can be made monomode over a large frequency range of the band gap by varying the width of the guide. The transmission through a guide containing a cavity can be made very selective and reduced to narrow peaks associated with some of the eigenmodes of the cavity. The effect of a side branch resonator is to induce zeros of transmission in the spectrum of the perfect guide that appear as narrow dips with frequencies depending upon the shape of the resonator and its coupling with the guide. We find perfect correspondences between the peaks in the transmission spectrum of a waveguide containing a cavity and the dips in the transmission of a cavity side coupled waveguide. Finally, when a gap exists in the spectrum of the perfect guide, a stub can also permit selective transmission of frequency in this gap. The results are discussed in relation with the symmetry of the modes associated with a linear guide or with a cavity.

Out-of-plane propagation of elastic waves in two-dimensional phononic band-gap materials

We have used a plane-wave-expansion model to study the out-of-plane propagation of elastic waves in a two-dimensional phononic band-gap material. The case of quartz rods embedded in an epoxy matrix has been computed. Band gaps for nonzero values of the wave-vector component parallel to the rods are shown to exist and are investigated. For wavelengths smaller than the period of the structure, modes are found that are localized in the epoxy intersites, and propagate perpendicularly to the plane of the structure.

Evidence of the existence of phononic band gaps: A practical example of a tunable sound insulation by a periodic device of rods

Based on the principle of phononic band gap materials, the control of acoustic frequency gaps by altering the geometry of the system is analyzed in the particular case of a set of parallel solid square-section columns distributed in air on a square lattice. This system is shown to be sensitive enough to the rotation of the columns to be considered for a practical sonic band gap width engineering. For different geometric configurations, experimental and theoretical results are presented and a discussion about the application of such structures as sound insulators is discussed. We acknowledge the use of the Namur Scientific Computing Facility (Namur-SCF), a common project between FNRS, IBM Belgium, and the Facultés Universitaires Notre-Dame de la Paix (FUNDP). [C. Goffaux acknowledges the financial support of the FIRST program of the Walloon Region Government and the Research and Development Centre of Cockerill-Sambre (ARCELOR Group).]